A derivation of the Vogel-Fulcher-Tammann relation for supercooled liquids

The non-Arrhenius Vogel-Fulcher-Tamman relation for the viscosity, eta, known for about 8 decades, describes simply one of the most characteristic features of supercooled liquids. It may be written eta = eta(0) exp [U/k(T-T-0)]. Using the Dyre et al. result demonstrating that U is proportional to the shear modulus, G, and the Interstitialcy Theory of Condensed Matter (ITCM) we derive this relation and obtain T-0/T-g = gamma/(gamma + 1) and U = U-0/(1 + gamma), where U-0 is the interstitialcy diffusion energy at the glass temperature. Here, gamma is a fragility softening parameter given by gamma=beta T-g(dc/dT)vertical bar T-g.beta is the shear susceptibility - d ln G/dc, and c is the interstitialcy concentration. gamma is also a fragility parameter ranging from 0 for strong materials to 3 or above for fragile ones. (C) 2010 Elsevier B.V. All rights reserved